Photon-Assisted Tunneling in Carbon Nanotube ... - ACS Publications

Article Cite This: ACS Appl. Electron. Mater. XXXX, XXX, XXX−XXX

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Photon-Assisted Tunneling in Carbon Nanotube Optical Rectennas: Characterization and Modeling Erik C. Anderson*,† and Baratunde A. Cola†,‡ †

George W. Woodruff School of Mechanical Engineering and ‡School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30313, United States

ACS Appl. Electron. Mater. Downloaded from pubs.acs.org by ALBRIGHT COLG on 04/30/19. For personal use only.

S Supporting Information *

ABSTRACT: We present optical characterization and modeling of carbon nanotube (CNT) rectennas featuring multiinsulator, metal−insulator−metal tunneling diodes. The diodes use four layers of Al2O3 and ZrO2 dielectrics to obtain strong nonlinearity and highly asymmetric current density at low turn-on voltage. The CNT rectenna devices show energy conversion in the full optical spectrum (404−980 nm). We introduce the theory of photon-assisted tunneling (PAT) to model the optical behavior based on unilluminated diode characteristics. Our model shows agreement between PAT and our experimental results, and fitting suggests a wavelength-dependent optical voltage. We discuss the impact of rectenna parameters and elucidate performance limits to our CNT rectenna device. KEYWORDS: metal−insulator−metal diodes, multiwall carbon nanotubes, optical rectenna, photon-assisted tunneling, solar energy conversion, vertical CNT arrays

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when operating near the CNT plasmon frequency.11,25 Generally, vertically aligned arrays tangled CNTs that are not uniform in length, which would affect their ability to behave as antennas over large areas. Also, close packing in arrays could cause strong diffusive scattering from nearby antenna interactions26 that may screen the CNTs and reduce field enhancement ordinarily seen in high-aspect-ratio CNTs.27 Thus, a full fundamental understanding of how CNT arrays function as antenna elements at optical frequencies is needed to gain a complete picture of their role in rectennas. Optical rectification also mandates a high-speed diode capable of converting the oscillating electric field in the antenna into d.c. photocurrent. The metal−insulator−metal (MIM) tunneling diode satisfies the ultrafast (femtosecond) switching time required for terahertz rectification.28,29 A MIM diode is a thin film technology composed of two electrodes separated by an insulator to create a potential energy barrier. Electron conduction is governed by nonlinear quantum tunneling through the barrier. Dissimilar electrodes form a potential gradient within the barrier that produces asymmetric

INTRODUCTION Optical rectennas have been garnering attention with promises of enhanced efficiency in visible and infrared energy conversion,1−6 photodetection,7,8 heat transfer and low utility waste heat harvesting,4,9,10 and wireless power transmission.1,11 Carbon-based nanomaterials are particularly interesting for high-frequency rectennas owing to their low cost, high mobility, and optical properties.3,12−14 For use in optical rectennas, graphene is an ideal material for geometric diodes and bowtie antennas.12,15,16 The transparency and exceptional conductivity also makes graphene an attractive electrode material.14,17 Meanwhile, the high aspect ratio of multiwall carbon nanotubes (CNTs) can be exploited in an asymmetric structure, producing a field enhancement that can increase rectifying performance.18 CNTs also make exemplary antenna elements, motivated by the extraordinary facility of CNTs to absorb electromagnetic energy in a broad spectrum19−22 and ability to be easily fabricated in vertically aligned arrays.23,24 As the CNT nanoantennas operate at infrared and visible frequencies, light−matter interaction governs the conversion of optical waves into a localized electrical field through each antenna.19,25 Our current understanding of the CNT antennas is based on classical dipole antenna theory, which may have limitations © XXXX American Chemical Society

Received: January 30, 2019 Accepted: April 16, 2019 Published: April 16, 2019 A

DOI: 10.1021/acsaelm.9b00058 ACS Appl. Electron. Mater. XXXX, XXX, XXX−XXX

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ACS Applied Electronic Materials

Figure 1. (a) Carbon nanotube rectenna device. (Inset) The tips of the CNTs are coated in a quad-insulator laminate of dielectric and capped with an Al top metal electrode to form a CNT/quad-insulator/metal (CI4M) tunneling diode. (b) SEM sideview of the CNT array coated with oxide and top metal. The oxide penetrates several microns into the array while conformally coating the CNTs. (Inset) The top metal coating the array is not planar but rather forms an interdigitated network of metal-coated CNTs with gaps between. (c) Energy band diagram of the CI4M structure featuring Al2O3/ZrO2/Al2O3/ZrO2 and an Al top electrode.

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current−voltage (I−V) response.30 Device resistance scales exponentially with barrier thickness, though mitigating resistance via a thin oxide layer comes at the expense of reduced nonlinearity and asymmetry.31,32 Fabrication limitations also arise with thin oxide layers. The operating regime of a rectenna is established by the 1 cutoff frequency of the diode: ωc = R C , given in terms of

THEORY We use the Tien-Gordon approach of PAT to elucidate the effect of optical illumination in our rectenna devices.41 The derivation of PAT for rectification has been rigorously covered in several other recent publications.42,43 Here, we provide an overview of PAT with more detail included in Section S.2. Upon illumination, the a.c. signal produced in the antenna causes a modulation in the Fermi level of the diode tunneling barrier. The overall voltage across the diode under highfrequency monochromatic light is Ṽ diode = V + Vωcos(ωt). V is the d.c. (i.e., dark) bias applied to the diode, and Vω is the a.c. voltage modulation induced by the electromagnetic field interacting with the electron distribution in the antenna material. Under PAT, we consider the quantization of the light, wherein an electron absorbs or emits a discrete number of photons, n, each with energy ℏω. This is reflected as a shift in the d.c. current−voltage response, ID(V), by a multiple of the photon voltage, Vph = ℏω/e. The photon-assisted (i.e., light) current, IL(V) is then the sum of all contributions of photonassisted electron states, weighed by the nth order Bessel function Jn(α):

A D

antenna resistance RA and diode capacitance CD. Ultrasmall capacitance poses a problem for most rectenna devices.33 We fabricate the diode at the tips of CNTs, where the CNT tip serves as both antenna and the lower metal junction (Figure 1(a,b)). This CNT−insulator−metal (CIM) diode concept mitigates antenna-to-diode ohmic loss, and more importantly, the ultrasmall tip area ensures attofarad capacitance.3,18 Because the work-function difference between most CNT and air-stable metals (Al for instance) is too low to generate enough asymmetry for optical rectification, manipulating the tunneling barrier via the insulator is needed. Tunneling diodes that combine multiple dielectrics have shown favorable performance over single-insulator diodes through more control of electron tunneling,31,34,35 an example of which is depicted in Figure 1(c). This work expands on our prior study of CIM diodes, which investigated multilayers of Al2O3 and ZrO2 to enhance electrical properties.36 We recently showed that more insulating layers generally enhanced the rectification ratio (i.e., asymmetry, A =

I(+V ) I(−V )

∞

IL(V ) =

∑

Jn2 (α)ID(V + nVph)

n =−∞

The argument α =

eVω ℏω

=

Vω Vph

(1)

is a measure of the a.c. field

strength. For quantum operation where Vω < Vph (i.e., α < 1), only the n = 0, ±1 Bessel terms are significant. For a diode with sufficient asymmetry and low turn-on voltage, the summation of the modulated I−V curves described in eq 1 allows positive current to flow under zero bias and provides power generation in the second quadrant. In practice, the illuminated I−V would vary from the prediction of PAT. This is due to the frequencydependent optical properties of the diode materials, which could cause substantial deviation in the shape and magnitude of the illuminated curves. As pointed out by Belkadi et al.,44 the high-frequency diode behavior may be significantly affected by frequency-dependent voltage division that alters the energy barrier of multi-insulator MIM structures. PAT theory predicts rectification with respect to the d.c. diode behavior, which is more feasible to measure than the high-frequency I−V characteristics that directly govern rectenna performance. The rectification process can be simplified to an equivalent electronic circuit by considering the antenna as an a.c. source

) without significantly affecting zero-

bias resistance relative to a single-insulator device of comparable thickness. The disparity between electron affinities (χAl2O3 ≈ 1.7 eV, χZrO2 ≈ 2.7 eV)37−39 facilitates resonant or step tunneling mechanisms that alter electron conduction.34,35,40 Improving step tunneling produces a greater forward current at lower bias while suppressing reverse bias current. Here, we demonstrate optical rectification over the full visible spectrum using our best diode structure, a quadinsulator (CI4M) diode with insulator stack composed of Al2O3/ZrO2/Al2O3/ZrO2 (see Figure 1 and Section S.1). The theory of photon-assisted tunneling (PAT) is applied to our measurements to model the CNT rectenna behavior and better understand the rectification mechanism and its ramifications. B


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Figure 2. (a) Dark I−V characteristics of the CI4M device with 16 nm Al2O3/ZrO2/Al2O3/ZrO2 insulator. Multiple repeat scans are shown to demonstrate scan consistency and stability over several days. Devices were very stable when scanning from ±1 V. (b) Fitting and extrapolation of dark I−V scans. Scanning from ±3 V shows a negative bias turn-on at −1 V, though higher bias caused more scan instability and likelihood of device failure. (Inset) Extrapolation past ±7 V was done by fitting a power law to each of the turned-on positive and negative bias regimes.

in parallel with the diode.7,43 The antenna source voltage (i.e., the optical voltage Vopt), depends on the input power to the antenna, Pin, and antenna radiation resistance, RA, by Vopt =

8PinRA

thermal evaporation to minimize penetration through the oxide. A device area of 0.07 cm2 was patterned with a shadow mask. Characterization. Electrical characterization was performed using a Keithley 2450 source monitor connected to a d.c. electrical fourprobe station. Optical characterization implemented monochromatic laser diodes connected to a thermoelectrically cooled mount (Thorlabs TCLDM9). Wavelengths from 404 nm (742 THz, 3.07 eV) to 980 nm (306 THz, 1.27 eV) were passed through a diffuser to produce uniform illumination over the device and minimize potential thermoelectric effects. All electrical and optical measurements were carried out in air at room temperature.

(2)

The a.c. voltage formed across the diode directly depends on this optical antenna voltage: stronger incident electromagnetic radiation produces a correspondingly higher a.c. field across the diode. Because there are several frequency-dependent factors at play in this system, such as high-frequency diode performance, antenna behavior, and antenna−diode coupling, we cannot accurately determine Vopt and Vω for our device. Instead, all unknown frequency dependencies will be treated together through a wavelength-dependent Vω. The external load, represented by the bias applied to the device, also plays a role in Vω. As a result of the nonlinear diode resistance, operating with fixed input power will require Vω to vary as a function of bias. This bias dependence is not immediately evident in the expression for the total timevarying diode voltage above and suggests PAT in eq 1 must account for Vω(V) via α = α(V). The process for estimating Vω(V) is covered in Section S.3. For an ideal, piecewise linear 1 diode, Vω ranges from 2 Vopt to Vopt.42,43,45 Under quantum operation, this produces a hump in the second quadrant of the illuminated I−V that leads to more efficient solar energy conversion.

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RESULTS AND DISCUSSION Dark Measurements. In this study, we use CI4M rectenna devices with 16 nm total insulator thickness consisting of Al2O3/ZrO2/Al2O3/ZrO2 quad-insulator laminate. Figure 2 illustrates the diode electrical response (i.e., the dark I−V rectenna characteristics). With our CI4M diodes, we achieve devices with great diode properties suitable for optical rectification: asymmetry surpassing 300 and high nonlinearity beginning at a low turn-on voltage of ∼0.3 V (Section S.1). Peak responsivity is 6 A/W. Despite the overall low conductivity, a consequence of the high thickness of insulation used, this structure gives superior device stability and favorable rectification parameters that are attractive for fundamental studies of device physics. We discussed previously that the CIM diode electrical behavior can be manipulated by altering the geometry of the tunneling barrier36 (Figure 1(c)). The tunneling behavior of a quad-insulator laminate is more complicated than that of a double insulator and can display several conduction mechanisms at various biases. Asymmetry is largely improved over that of single- and double-insulator diodes. This is because the thin outer layer of ZrO2 in our CI4M initiates step tunneling at lower bias; reverse bias current is also suppressed on account of the overall thicker oxide compared to a typical CI2M. With four dielectric layers, this diode might experience additional step tunneling in either direction. This is perhaps demonstrated by the abrupt increase in reverse bias current at −1 V. We also suspect it could be from resonant tunneling because of a quantum well forming within the shallow inner ZrO2 layer (layer #2) sandwiched between layers of Al2O3. Because our devices are not stable past ±3 V, we do not know what conduction mechanisms dominate at higher bias, so for PAT theory, we estimate the high-bias diode behavior by

EXPERIMENTAL METHODS

Device Fabrication. Carbon nanotube rectenna devices were fabricated using similar methods to those of previous reports3,32,36 (Figure 1(a)). Multiwall carbon nanotubes were grown on SiO2coated Si. Ti/Al/Fe (100/10/3 nm) was deposited as the bottom electrode with Fe acting as the CNT catalyst. The vertical array of CNTs was grown using low-pressure chemical vapor deposition with C2H2 carbon source gas (Aixtron Black Magic). Growth time around 180 s produces an array with heights around 10−30 μm, 8 nm diameter, and ∼6 walls (Figure 1(b)). To expose the inner multiwalls, the CNT tips were etched away with 30 s of O2 plasma. The CNT array was then conformally coated with multiple oxide layers by atomic layer deposition at 250 °C. Layers were formed by cycling precursors of trimethylaluminum (for Al 2 O 3 ) or tetrakis(dimethylamide) zirconium (for ZrO2) along with H2O vapors. Extended purge times were used so precursors could infiltrate the CNT array, giving an average coating of 4 nm per 40 cycles. The top electrode metal was a 50 nm planar equivalent of Al deposited using C


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Figure 3. (a) Rectenna I−V characteristics under illumination with a wavelength range of 404−980 nm. Incident power is fixed at 5 mW/cm2 with a diffuser used to illuminate uniformly over the device area. (b) High-resolution I−V scans near zero bias. The increase in forward bias current and second quadrant power generation are evidence of optical rectification. (c,d) I−V curves and short-circuit current, Isc, with varying input power (λ = 638 nm). (d) Time-dependent Isc with varying laser intensity. Optical response is stable over time, and measurements are well above the noise threshold. ON/OFF switching shows that thermal relaxation from device heating does not affect optical response.

insulator CI2M rectenna reported previously.32 These devices are potential candidates for detection despite the low current. Figure 3(c,d) shows a rise in current that scales with illumination intensity. The measured optical response is very stable in time (Figure 3(d)). Light−matter interactions in the CNT antenna cause a dependency of optical source voltage on laser intensity, which ultimately affects the optical response through Vω.33 There is widespread concern that temperature gradients could induce thermal voltages that may be misconstrued for rectification.46,47 We provide evidence (Section S.5) to rule out thermal behavior using an IR camera to measure surface temperature across an illuminated device. We did not observe a significant temperature gradient that would lead us to expect thermal effects, and the fast ON/OFF switching in Figure 3(d) shows no time-dependent response that would occur from heating of the device. Photon-Assisted Tunneling Characterization. In this section, we use PAT theory to model the illuminated I−V rectenna based on our diode’s dark I−V behavior according to eq 1 (see Section S.6). By comparison to our experimental light measurements, we gain a better understanding of the CNT rectenna behavior. This also elucidates loss mechanisms such as transmission loss through the top electrode and antenna−diode coupling mismatch. Modeling the light characteristics with high photon energy (Eph ≈ 3 eV at λ = 404 nm) requires diode I−V to be scanned over a correspondingly large bias. We managed to scan ±3 V before reaching device breakdown. A sufficient I−V window

extrapolating the diode I−V (Figure 2(b)). This is covered in Photon-Assisted Tunneling Characterization Section. Optical Measurements. Here, we present optical measurements of our CI4M rectenna devices across the visible spectrum. Devices are illuminated with 5 mW/cm2 incident laser power over a wavelength range of 404−980 nm (Figure 3(a,b)). I−V characteristics show a large increase in the forward bias current under illumination and a shift into the second quadrant, both indicators of the rectification mechanism as discussed above. The optical response exhibits wavelength dependence, though the trend is not monotonic with frequency. Further, accounting for wavelength-dependent transmission loss in the top metal did not simplify this trend, as elaborated in Section S.4, so calculations are left in terms of the incident laser intensity. The effect of photon energy on the rectification mechanism is explored in depth in the next section. For the wavelengths tested, we see the maximum performance occurring at 638 nm: the open-circuit voltage is Voc = −95 mV, and the short-circuit current is Isc = 7.6 nA/cm2; with respect to incident intensity total conversion efficiency, η=

Pout(MPP) , Pin

which equals 3 × 10−6% at the maximum

power point (MPP). Efficiency is low primarily because of large resistance associated with the 16 nm thick insulator that was chosen to maximize asymmetry, device stability, and breakdown voltage for this study of fundamental device physics. Still, open-circuit voltage responsivity is 250 V/W for our 0.07 cm2 device, which is larger than that of the doubleD


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Figure 4. High-resolution I−V behavior of the rectification response at λ = 638 nm and 5 mW/cm2 intensity. Markers represent dark (black) and light (red) scan data. (a) The predicted optical response (blue line) based on the theory of PAT was determined by treating the diode voltage, Vω, as a constant parameter and fitting to the light scan data. In the case of 638 nm, the PAT model yielded Vω = 68 mV. (b) A better prediction of the optical response was achieved by assuming bias-dependent Vω (i.e., constant power operation). Fitting for Vω(V) gives a mildly linear trend from 58 mV at Voc to 81 mV at zero bias.

Figure 5. (a) Diode voltage, Vω, is determined by fitting the PAT model to illumination I−V data for constant power operation. The figure shows how the a.c. diode voltage varies with bias by depicting Vω(V) at Voc and Isc. Cubic splines (solid lines) are used to interpolate Vω across the wavelength range for use in the PAT model. Vω under constant a.c. voltage operation is shown (open squares) for reference. (b) Prediction of Vω by fitting eq 3 to Vω(Voc) data. Dominant behavior from optical voltage and antenna−diode coupling efficiency depicted by shaded and unshaded regions, respectively. The cutoff frequency is estimated at 3.25 eV.

for PAT convergence calls for extrapolation. Power law fitting is implemented to separately fit the high-bias positive and negative I−V regimes and extrapolate the dark current past ±7 V (Figure 2(b)). This approach accommodates Bessel terms at least to order 2 (Section S.7). Unlike the photon voltage, which we readily control by choosing the incident light source, Vopt and Vω are difficult to estimate in our PAT prediction because of uncertainty with input parameters such as input power and antenna resistance. There are several significant assumptions associated with calculating the optical voltage in eq 2, namely, that the actual power absorbed by the CNTs is not known well, and radiation resistance of the antenna is likely wavelength-dependent. Hence, Pin and RA must be lumped together and fit for via Vopt. More importantly, because the incident power of the light source is constant throughout I−V scanning, Vω can change with bias because of the nonlinear diode resistance responsible for a.c. power dissipation.45 The a.c. power in the diode is 1 I V .7 Under constant a.c. power operation, the bias2 ω ω dependent diode voltage, Vω(V), can be estimated according to Iω, the time-dependent a.c. current that arises from higherorder harmonics of PAT through the diode. Iω and the process for determining Vω(V) is outlined in Section S.3. In short, we

demonstrate below that we can achieve better agreement to experimental light I−V when introducing mild bias dependency in Vω. A comparison of the rectification response for experimental data versus the traditional PAT prediction is shown in Figure 4 for 638 nm light. The fixed a.c. diode voltage of Vω = 68 mV is found from fitting to the light data (Figure 4(a)). Photon energy of 1.94 eV gives quantum operation (α = 0.035), and Bessel terms up to fourth order were used, keeping error from truncating higher-order terms below 1%. The model demonstrates reduction in zero-bias resistance and lowering of responsivity that is expected.3 Still, the model underV estimates the current (e.g., the secant resistance R sec = Ioc sc

predicted by PAT is distinctly higher than our experimental data). Further, the model deviates considerably when attempting to predict optical behavior at high bias (Section S.9). This is likely attributed to a failure of our extrapolated I− V to predict the true diode characteristics at high bias and at optical frequencies. By adjusting our model to solve for bias-dependent Vω(V), we reach excellent agreement between illuminated I−V scans and the PAT prediction (Figure 4(b)). In the case of λ = 638 nm, Vω varies from 58 mV at Voc = −95 mV to 81 mV at zero E


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ACS Applied Electronic Materials bias. This supports the idea that these devices operate under a constant input power condition rather than constant a.c. voltage and highlights the importance of the a.c. resistance in designing to an intended operating point for optimal power transfer. We next apply the PAT model to illustrate how both photon energy and input power affect the optical response. For wavelength-dependent optical excitation, the diode voltage is estimated by assuming bias dependence and individually fitting the PAT model to the I−V of each wavelength that was tested (Figure 5(a)). We find less significant bias variation as the photon energy is lowered. We use a simple spline to interpolate wavelength-dependent Vω through photon energy up to 3.5 eV. From Figure 5(a), a linear trend of Vω(Vph) is observed up until 2.2 V. The likely explanation for this linearity is that the CNTs act as dipole antennas. Prior to this study, we assumed our antenna resistance was around 100 Ω, consistent with the literature.3,7,25,48,49 Unlike bowtie antennas,12,15,50,51 our CNTs likely act as dipole nanoantennas such that RA will change with frequency. Classically, the resistance of a dipole is proportional to the frequency squared (i.e., RA ∝ ω2).52 Our definition of Vopt in eq 2 therein suggests that the dipole antenna voltage is linear with frequency, which would proportionately affect Vω in the diode. We also postulate that deviation from the linearity at higher frequencies arises from antenna−diode coupling loss. As shown in related rectenna analysis,2,7 the antenna-to-diode coupling diminishes after a cutoff frequency, wherein we can estimate the diode voltage relative to the antenna optical voltage through Vω(ω) =

Figure 6. Comparison of PAT theory and measured (a) short-circuit current, Isc, and (b) open-circuit voltage, Voc. Blue diamonds show experimental data points; the dashed line shows the simulated PAT model with fixed, frequency-independent diode voltage, using 808 nm as the reference wavelength from Figure 5 (Vω = 60 mV at 0 V bias); the solid line shows the PAT model with Vω(Vph) fitted at each wavelength.

leads the drop off in performance. If this is the case, then one solution to improve the operating regime is by lowering capacitance to increase ωc. The peak optical conversion efficiency we predict from PAT is 3.6 × 10−6%, which is comparable to those of our prior reports3,32 (see Table S1). We suspect that the actual input power absorbed by the CNTs is much less than the power we measure as incident upon the device surface. Even though rectenna conversion efficiency is still low, Voc is large enough to give these CNT devices potential use as optical detectors. The Voc here is several orders of magnitude higher than that of the first CNT rectenna reported by Sharma et al., which used a single insulator capped with Ca to produce low-work-function asymmetry.3 This is accredited to the improvement via the quad-insulator device structure.36 However, low current remains a hindrance to overall efficiency. Isc is lower than that of prior reports because of the high diode resistance associated with 16 nm thick insulation. Because this report is focused on understanding how our rectenna devices operate in light of PAT, the choice of a thick insulator is subsequently motivated by the excellent diode stability and broad scanning bias range. Next, we determine the effect of light intensity on illumination response by applying PAT theory through a range of incident laser powers according to eq 2. Figure 7 shows Isc and Voc at the representative wavelength of 638 nm (1.94 eV). There is excellent agreement between measurements and theory. Because the input power drives the optical voltage, greater laser intensity increases the rectified power generated in the second quadrant. The linear dependence between Isc and incident power shown in Figure 7(a) further supports optical rectification, owing to the fact that rectified current should be proportional to power delivered to the

Vopt(ω) (1 + (ωRA(ω 2)C D)2 )1/2

(3)

We fit eq 3 to the results of our PAT fitting (Figure 5(b)) with further details provided in Section S.10. When assuming a frequency-dependent optical voltage according to a dipole model, eq 3 strongly matches the estimated values of Vω throughout the entire range of optical measurements. This provides convincing evidence of the role of the CNT array as dipole nanoantennas. Further, eq 3 allows us to estimate a cutoff frequency at 3.25 eV (785 THz). From our estimated Vω(Vph), PAT theory generates peaks in Voc and Isc around 2.2 eV, corresponding to our measurements (Figure 6). For comparison, considering wavelength-independent Vω produces a maximum Voc and Isc that are in the infrared, around 0.8 eV (1550 nm). The latter result is attributed to the reverse bias turn-on voltage of the diode suppressing rectification asymmetry. When photon energy exceeds this reverse bias turn-on, there is no longer asymmetric tunneling of photon-assisted electrons, and hence, the a.c. current passing through the diode is no longer rectified. We confirm this by examining the diode asymmetry (Figure S.1), which exhibits a peak at ∼0.8 V that matches the infrared peak in optical performance. Thus, we highlight the importance of manipulating the diode I−V: suppressing the reverse bias turn-on is a route to enhance rectenna operation. Introducing wavelength dependence into Vω shifts the overall performance to higher photon energy in the visible regime. Rather than acting as an artifact of the diode I−V, we suspect the peak occurring at 2.2 eV arises by surpassing the diode’s cutoff frequency: when the frequency of illumination exceeds ωc the diminishing antenna−diode coupling efficiency F


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bias current is important to minimize loss at high photon energy, whereas low turn-on enables efficient operation at lower photon energy, particularly when incident intensity is low enough to maintain quantum operation. Choosing electrodes that are more transparent yet conductive remains essential to mitigate optical and ohmic power losses. Lastly, better understanding of the CNT array as antenna elements is needed to optimize the optical voltage through antenna efficiency and radiation resistance.

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CONCLUSIONS Our results show evidence for rectification in the full range of optical frequencies using a carbon nanotube array rectenna featuring a CI4M diode. The novel quad-insulator tunneling structure generates excellent diode asymmetry with a low turnon suitable for rectification. We use PAT theory to model the illuminated behavior of rectenna devices based on dark I−V measurements. The model matches predictions to experimental measurements across the optical spectrum. Our predictions provide further evidence of the rectification mechanism in our CNT rectenna devices. By fitting the model to experiment, we estimate the diode voltage and gain insight into several rectenna parameters of interest. The PAT prediction fits measurements better when we assume bias-variable a.c. diode voltage under fixed input power operation (5 mW/cm2). We also see a deviation with wavelength that can be accounted for through a combination of frequency-dependent optical voltage, antenna−diode coupling efficiency loss near cutoff frequency, and frequencydependent dielectric properties. This trend provides strong evidence of the role of the CNT as dipole antenna and enables an estimate of the cutoff frequency to be 780 THz (3.25 eV). We use this model to assess performance limits and determine areas of improvement for future generations of devices. The current structure has a peak performance around 638 nm with Voc exceeding −95 mV and η ≈ 3 × 10−6%. Our model suggests that this could be improved by engineering the diode with lower resistance and capacitance, suppressing the reversebias current, and using top electrode materials that maximize light collection into the CNT array. Further refinement of the rectenna model is needed to understand and accurately depict operation of the CNT antenna at optical frequencies and any frequency dependence therein.

Figure 7. Laser power dependence on (a) short-circuit current (Isc) and (b) open-circuit voltage (Voc) at a wavelength of 404 nm. Comparison of experimental data versus the PAT model is shown with the input power for the PAT model scaled up by a factor of 87 to fit the experimental data.

diode.7 This is also consistent with the enhanced photocurrent we observed in Figure 3(c).47 The short-circuit current response is 1.5 μA/W. In contrast, Voc approximately depends upon the square root of incident power. This Voc relationship heuristically follows the power-dependent optical voltage that drives PAT. We note that the input power of the PAT prediction displayed in Figure 7 was scaled up by a factor of 87 to coincide with the experimental data. If antenna resistance around 100 Ω is assumed, then eq 2 predicts input power that is much lower than our measured incident laser power to fit PAT to the data. This is reasonable based on the inevitable power losses associated with transmission of the incident radiation into the array and absorption by the CNT antennas. We estimate that transmissivity of the Al electrode is below 6% and features a mild wavelength dependence (Figure S3). Accounting for transmission would be misleading, because there are complications such as the light transmitting through gaps in the top metal coating (see inset of Figure 1(b)). Other power loss mechanisms, for instance, the antenna efficiency, can only be speculated but likely have significantly adverse effects on our present device performance. On the basis of PAT, efficiency can be improved by optimizing the diode voltage under constant a.c. power. This requires tuning the dark I−V to affect the semiclassical resistance. Engineering the CIM diode I−V is perhaps the most direct route to better rectenna efficiency. Maximizing the diode conductivity generally leads to better response across the board. However, thinning the tunneling barrier to reduce diode resistance similarly increases leakage current.32 Additionally, the effect of a thinner insulator on capacitance and therefore the cutoff frequency cannot be neglected. Instead, implementing a multi-insulator laminate is a route to achieve high asymmetry with low turn-on voltage.36 Suppressing the reverse

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsaelm.9b00058.

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Diode electrical characterization, optical transmission measurements of the Al electrode, infrared images and evidence to rule our thermoelectric behavior, a short derivation of photon-assisted tunneling current used to model optical rectification, verification of the photonassisted tunneling model, error analysis of the model, and estimation of cutoff frequency (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Erik C. Anderson: 0000-0003-0143-7135 G


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ACS Applied Electronic Materials Notes

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The authors declare the following competing financial interest(s): Georgia Tech has applied for a patent, application no. PCT/US2013/065918, related to the design methods and materials produced in this work.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation Graduate Research Fellowship Program (no. DGE-1650044) and the Alan T. Waterman Award (no. 1748413). The authors thank the staff of the Institute for Electronics and Nanotechnology at Georgia Institute of Technology for providing equipment support. E.C.A. particularly thanks Dr. Thomas L. Bougher for assistance with the PAT code and for many useful discussions.

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